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Your code book must be different than mine. I see nothing in 240.4 that allows a 14 AWG to be protected by a 20 AMP OCPD.
Can you quote an article? NO dubs, no opinions, just facts!
EDIT 240.4(E)(1) does not apply. (3) does.
How can you say 240.4(E)(1) does not apply?
It specifically permits tap conductors to be protected against overcurrent in accordance with 210.19(A)(3) and (A)(4). It does not say in accordance with their Exceptions.
Anyway....
Let's examine compliance per 240.4(E)(3), as specifically permitting a #14 tap conductor to be protected against overcurrent in excess of the 240.4(D)(3) restriction of 15A...
240.21 Location in Circuit... (A) though (H) specify conditions where ocp does not have to be located where an ungrounded circuit conductor receives its supply. It goes on to say conductors meeting the conditions
shall not supply another conductor except through an ocpd.
For this discussion, only
(A) applies:
Branch-Circuit Conductors. Branch-circuit tap conductors meeting the requirements specified in 210.19 shall be permitted to have overcurrent protection as specified in 210.20.
Note there is no reference to exceptions where the term "tap" is used as being the only applicable requirements. 210.19 and 210.20 are referenced in their entirety. Being we already know our #14 is compliant with 210.19 (i.e. sufficiently sized for its load), ocp is determined under 210.20. So we go to 210.20 to see if a 20A branch-circuit ocpd is compliant.
Verifying compliance with 210.20(A)... good to go because we have already determined the load served by our #14, calculated non-continuous plus 125% continuous, is 20A or less.
Next we verify compliance with 210.20(B). Because 210.20(B) sends us back to where we started (240.4), it is rendered moot the second time around because we'd just end up back here at 210.20(B) again anyway.
Verifying 210.20(C) involves equipment listed in Table 240.3. So far, our discussion is not about connecting to such equipment, so (C) does not apply.
Verifying 210.20(D), it says the ocp rating or setting shall not exceed values specified in 210.21 for outlet devices. 210.21 has no requirements for conductor size or ampacity.
So it looks like as long as we do not supply another conductor, no load-end ocpd is required for the #14 tap conductor.
We continue to be compliant with all requirements having a #14 on a branch circuit protected with a 20A ocpd, even by way of 240.4(E)(3)!!!
EDIT TO ADD: I used the word compliant above. Keep in mind I am only using the word compliant in regards to the literal interpretation of Code, not the consensus nor intent nor what I actually practice in the real world.